Question

Here are the equations of five straight lines.
Line A. y + 3x = 4
Line B. 2y = x + 1
Line C. y + 2x = 3
Line D. y = 4x - 2
Line E. 2y = 2x – 1
Two of these lines are perpendicular.
Write down the two perpendicular lines.

Answer 1

Answer:

Step-by-step explanation:

perpendicular lines have negative reciprocal slopes. So we will put each equation in y = mx + b form, and compare the slopes. The slopes, in y = mx + b form, are in the m position.

Line A : y + 3x = 4....y = -3x + 4.....slope is -3

Line B: 2y = x + 1.....y = 1/2x + 1/2.....slope is 1/2

Line C : y + 2x = 3.....y = -2x + 3......slope is -2

Line D: y = 4x - 2.....slope = 4

Line E: 2y = 2x- 1......y = x - 1/2.....slope is 1

take a look at Line B. it has a slope of 1/2.....to find the negative reciprocal, all that means is flip the slope and change the sign.

slope 1/2......flip it.....2/1.....change the sign...-2/1 or just -2.

this means that a line perpendicular to this one will have a slope of -2....and thats the slope Line C has.

so line B and line C are perpendicular <=== because there slopes are negative reciprocals of each other.....slope 1/2 and slope -2